The Thunder Plains Lightning Rod Towers are in need of calibration.
In order to calibrate them, you will have to enter a series of commands in the form of button presses.
You will be allowed 2 misses per try, upon the 3rd miss you will have to start over.
In general, the southern towers are easier than the northern ones.
There are 10 towers with 3 types to deal with: 3 for Rikku, 3 for Paine and 4 for Yuna.

repeat button sequence in the correct order. You cannot walk to Tower 10 but you can do a remote calibration by going to a spot on the left side just below the shelter.

Tower

Number of Hits

Number in Sequence

Possible Buttons

Tower 3

0-10

2

[Triangle] [Circle] [X] [Square]

11-25

3

[Triangle] [Circle] [X] [Square]

26-30

4

[Triangle] [Circle] [X] [Square]

Tower 6

0-10

2

[Triangle] [Circle] [X] [Square] [D-pad]

11-25

3

[Triangle] [Circle] [X] [Square] [D-pad]

26-30

4

[Triangle] [Circle] [X] [Square] [D-pad]

Tower 9

0-10

2

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1]

11-20

3

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1]

21-25

4

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1]

26-30

5

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1]

Tower 10

0-10

2

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1] [L2] [R2]

11-15

3

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1] [L2] [R2]

16-20

4

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1] [L2] [R2]

21-25

5

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1] [L2] [R2]

26-27

6

[Triangle] [Circle] [X] [Square] [D-pad] [L1] [R1] [L2] [R2]

Speak to the Al Bhed in the Travel Agency to check on your progress.
Once you have attempted every tower and perfectly calibrated at least 5 of them, he'll give you the Samurai's Honor grid.

This sidequest is only available in Chapter 2 and Chapter 3.
The prizes that are obtained in Chapter 5 during A Fallen Genius? are dependant on how well you do in this sidequest, so try to calibrate as much as you can.